Modeling of encapsulated cell systems

Tissue engineered substitutes consisting of cells in biocompatible materials undergo remodeling with time as a result of cell growth and death processes. With inert matrices that do not directly influence cell growth, remodeling is driven mainly by the concentration of dissolved oxygen (DO). Insulin-secreting cell lines encapsulated in alginate-based beads and used as a pancreatic substitute represent such a case. Beads undergo remodeling with time so that an initially homogeneous distribution of cells is eventually replaced by a dense peripheral ring of primarily viable cells, whereas inner cells are mostly necrotic. This paper develops and analyzes a mathematical model of an encapsulated cell system of spherical geometry that tracks the viable and dead cell densities and the concentration of DO within the construct as functions of radial position and time. Model simulations are compared with experimental histology data on cell distribution. Correlations are then developed between the average intrabead DO concentration (AIDO) and the total viable cell number, as well as between AIDO and the radial cell and DO distributions in beads. As AIDO can be measured experimentally by incorporating a perfluorocarbon emulsion in the beads and acquiring 19F nuclear magnetic resonance (NMR) spectroscopic data, these correlations can be used to track the remodeling that occurs in the construct in vitro and potentially in vivo. The usefulness of mathematical models in describing the dynamic changes that occur in tissue constructs with time, and the value of these models at obtaining additional information on the system when used interactively with experimental measurements, are discussed.